login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298122 a(n) is the number of n nonintersecting arches above the x-axis that start and/or end with an arch length equal to one and have floor((n+2)/2) arches starting in odd numbered positions. 0
1, 1, 2, 5, 11, 34, 90, 300, 875, 3038, 9408, 33516, 108108, 392040, 1302444, 4785066, 16256955, 60324550, 208579800, 780088452, 2735682092, 10296854984, 36532677272, 138231751840, 495241833996, 1882201158264, 6799413051200, 25939319270000, 94374970110000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(1) = a(2) = 1, a(3) = 2; for n > 3, a(n) = 2*(C(n-1, floor((n-1)/2))*C(n-2, floor((n-2)/2)) - (C(n-1, floor((n-2)/2))*C(n-2, floor((n-3)/2)))) - (C(n-3, floor((n-1)/2))*C(n-2, floor((n-1)/2))/(floor((n-1)/2)+1)).
EXAMPLE
Example: For n = 4 the a(4) = 5 solutions are as follows. (The numbers under the arches represent arches starting in an odd-numbered position on the x-axis.)
/\ /\
//\\ /\ /\ //\\ /\
///\\\/\, //\\ /\ /\, /\//\\/\, /\///\\\, /\/\//\\.
1 3 7 1 5 7 1 3 7 1 3 5 1 3 5
CROSSREFS
Sequence in context: A080068 A226919 A307316 * A196690 A101834 A117758
KEYWORD
nonn
AUTHOR
Roger Ford, Jan 12 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 26 09:41 EST 2024. Contains 370338 sequences. (Running on oeis4.)